Let λ ∈ ℝ and let the equation E be | x | 2 - 2 | x | + | λ - 3 | = 0 . Then the largest element in the set S = { x + λ : x is an integer solution of E } is ______

Question

Let λ ∈ ℝ and let the equation E be | x | 2 - 2 | x | + | λ - 3 | = 0 . Then the largest element in the set S = { x + λ : x is an integer solution of E } is ______,

MARKS App · Accepted Answer

Given: | x | 2 - 2 | x | + | λ - 3 | = 0 ⇒ | λ - 3 | = x 2 - x At λ = 3 , x = 0 and 2 , At λ = 4 or 2 , then, x = 1 or - 1 So, maximum value of x + λ = 5 when x = 1 and λ = 4 .

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